17.2 Plans and elevations — Learn

Prerequisites: recognise rectangles, triangles and cuboids; use a square grid.

Objectives: interpret a plan and elevations, then construct these views from a 3D shape. This page covers G13.

Views of a solid

A plan is the view from directly above. A front elevation is the view from directly in front. A side elevation is the view from one side. Each view is flat, so depth or height can disappear. Hidden edges are not normally shown unless the question asks for them.

Worked example. A cuboid measures $5$ cm wide, $3$ cm deep and $2$ cm high.

• From above, you see the top rectangle: $5$ cm by $3$ cm.
• From the front, you see width and height: $5$ cm by $2$ cm.
• From the side, you see depth and height: $3$ cm by $2$ cm.

To construct the views, keep the same scale and align corresponding edges. Label the direction of each view before drawing.

A stepped solid can have a plan that shows its footprint while the elevations show different heights. Read a plan square by square, then transfer each height to the matching position in the elevation.

Watch out. The plan does not show height. A $2$-cm-high block and a $5$-cm-high block can have the same plan. Use the elevations to recover height.

Progress check

The garden is $24$ m by $18$ m. At a scale of $1$ cm for $3$ m, work out the plan dimensions. Then state which view would show the $18$ m side.

You should now be able to

• identify plans and front or side elevations;
• interpret dimensions in each view;
• draw aligned views of a cuboid and a stepped solid;
• explain which dimension can be read from each view.